Contents Online
Mathematical Research Letters
Volume 26 (2019)
Number 3
A note on self orbit equivalences of Anosov flows and bundles with fiberwise Anosov flows
Pages: 711 – 728
DOI: https://dx.doi.org/10.4310/MRL.2019.v26.n3.a3
Authors
Abstract
We show that a self orbit equivalence of a transitive Anosov flow on a $3$-manifold which is homotopic to identity has to either preserve every orbit or the Anosov flow is $\mathbb{R}$-covered and the orbit equivalence has to be of a specific type. This result shows that one can remove a relatively unnatural assumption in a result of Farrell and Gogolev [9] about the topological rigidity of bundles supporting a fiberwise Anosov flow when the fiber is $3$-dimensional.
The second author was partially supported by Simons grant 427063.
Received 3 February 2017
Accepted 8 October 2018
Published 25 October 2019